Adaptations of the [14C]deoxyglucose method for the quantitative determination of local rates of cerebral glucose consumption and of the [14C]iodoantipyrine method for determination of local rates of cerebral blood flow for human use with PET and [18F]fluorodeoxyglucose and 15 O- labeled water, respectively, have presented some special problems. Due to the limited spatial resolution and partial volume effects of PET scanners, measurement of radioactivity in homogeneous tissues is rarely, if ever, achieved. Hence one of the explicit assumptions of both methods, that of tissue homogeneity, is not met; this assumption is frequently forgotten or ignored, and serious misinterpretations and misuses of the methods have resulted. We have examined the effects of tissue heterogeneity on determinations of local cerebral blood flow and glucose utilization and have developed mathematical models to explicitly account for the tissue heterogeneity. These models have been validated in simulation studies and are currently being validated in human and animal studies. In addition, we are assessing the special time constraints for the use of [18F]fluorodeoxyglucose with PET in man. The results of these studies will provide us with the necessary information for choosing the most appropriate kinetic models and optimal experimental protocols for the measurement of glucose utilization and blood flow with PET.